Question

The distance from the dwarf planet Pluto to the sun is 4.43 × 109 km at perihelion and 7.37 × 109 km at aphelion. Find the eccentricity e of Pluto's orbit. (Round your answer to three decimal places.) e =

Answer 1

0.249

Step-by-step explanation:

Perihelion = 4.43 x 10^9 km

Aphelion = 7.37 x 10^9 km

Let e be the eccentricity and a be the length of semi major axis.

The relation between the semi major axis, perihelion and aphelion s given by

Semi major axis = half of sum of perihelion and aphelion

`a = (4.43+7.37)/(2)*10^(9)`

a = 5.9 x 10^9 km

The relation between the perihelion, semi major axis and the eccentricity is given by

Perihelion = a (1 - e)

4.43 x 10^9 = 5.9 x 10^9 (1 - e)

0.751 = 1 - e

e = 0.249